Probability Theory


The module is available as a YouTube playlist and as a short course with quizzes on Learning Hub (syllabus shown to the right)

YouTube

Overview

This 6 week short course in the Science of Information Series provides a critical foundation for understanding more advanced science of information topics. Probability theory is essential to conducting quantitative analysis of large sets of data, and in applying to descriptions of complex systems given only partial knowledge of their state.

Estimated time required: 2 hours per week.

Author

Mark Daniel Ward
Associate Professor
Statistics
Purdue University

Syllabus/Suggested Schedule

Events & Outcomes
Probability Defined
Sample Space & Outcomes
Additional Insights & Examples
Independent Events and Disjointness
Conditional Probability
Independence
Baye's Theorem
Introduction to Random Variables Part 1
Introduction to Random Variables Part 2
Probability Mass Function
Cumulative Distribution Function
Joint Cumulative Distribution Function
Independence of Random Variables
Conditional Mass Function & Random Variables
Finding Expected Value of Random Variable
In depth Example of Finding Expected Value Using Dice
In depth Example of Finding Expected Value Playing Roulette
Calculating Entropy
Example Using a Biased Coin
Example Using Random Words
Discrete Values of Random Variables
Entropy of Random Variables